/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: f(0()) -> 0()
    2: f(s(0())) -> s(0())
    3: f(s(s(x))) -> p(h(g(x)))
    4: g(0()) -> pair(s(0()),s(0()))
    5: g(s(x)) -> h(g(x))
    6: h(x) -> pair(+(p(x),q(x)),p(x))
    7: p(pair(x,y)) -> x
    8: q(pair(x,y)) -> y
    9: +(x,0()) -> x
    10: +(x,s(y)) -> s(+(x,y))
    11: f(s(s(x))) -> +(p(g(x)),q(g(x)))
    12: g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #h(x) -> #+(p(x),q(x))
   #2: #h(x) -> #p(x)
   #3: #h(x) -> #q(x)
   #4: #h(x) -> #p(x)
   #5: #f(s(s(x))) -> #+(p(g(x)),q(g(x)))
   #6: #f(s(s(x))) -> #p(g(x))
   #7: #f(s(s(x))) -> #g(x)
   #8: #f(s(s(x))) -> #q(g(x))
   #9: #f(s(s(x))) -> #g(x)
   #10: #g(s(x)) -> #+(p(g(x)),q(g(x)))
   #11: #g(s(x)) -> #p(g(x))
   #12: #g(s(x)) -> #g(x)
   #13: #g(s(x)) -> #q(g(x))
   #14: #g(s(x)) -> #g(x)
   #15: #g(s(x)) -> #p(g(x))
   #16: #g(s(x)) -> #g(x)
   #17: #+(x,s(y)) -> #+(x,y)
   #18: #g(s(x)) -> #h(g(x))
   #19: #g(s(x)) -> #g(x)
   #20: #f(s(s(x))) -> #p(h(g(x)))
   #21: #f(s(s(x))) -> #h(g(x))
   #22: #f(s(s(x))) -> #g(x)
Number of SCCs: 2, DPs: 5
  SCC { #17 }
POLO(Sum)... succeeded.
      h 	w: 0
      q 	w: 0
      s 	w: x1 + 1
      pair	w: 0
      #p 	w: 0
      f 	w: 0
      p 	w: 0
      0 	w: 0
      #h 	w: 0
      #f 	w: 0
      #g 	w: 0
      #q 	w: 0
      + 	w: 0
      g 	w: 0
      #+ 	w: x2
    USABLE RULES: { }
    Removed DPs: #17
Number of SCCs: 1, DPs: 4
  SCC { #12 #14 #16 #19 }
POLO(Sum)... succeeded.
      h 	w: 0
      q 	w: 0
      s 	w: x1 + 1
      pair	w: 0
      #p 	w: 0
      f 	w: 0
      p 	w: 0
      0 	w: 0
      #h 	w: 0
      #f 	w: 0
      #g 	w: x1
      #q 	w: 0
      + 	w: 0
      g 	w: 0
      #+ 	w: 0
    USABLE RULES: { }
    Removed DPs: #12 #14 #16 #19
Number of SCCs: 0, DPs: 0